The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005. Use the Poisson distribution to approximate the probability that among 14,000 cars passing through this tunnel, exactly two will have a flat tire. Round your answer to four decimal
Places.
A) 0.1460
B) 0.8783
C) 0.1217
D) 0.1947
E) 0.1703

Question

Quizplus · Accepted Answer

The Poisson distribution formula is $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of successes in the given interval (in this case, the mean number of cars having a flat tire), and $k$ is the number of successes we're interested in (in this case, exactly 2 cars having a flat tire). Here, $\lambda = 14,000 \times 0.00005 = 0.7$. Plugging these values into the formula gives $P(X=2) = \frac{e^{-0.7} \cdot 0.7^2}{2!} \approx 0.1217$.

The Probability That a Car Will Have a Flat Tire